TSTP Solution File: SWW196+1 by Twee---2.4.2
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- Process Solution
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% File : Twee---2.4.2
% Problem : SWW196+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:54:23 EDT 2023
% Result : Theorem 114.13s 15.07s
% Output : Proof 114.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW196+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 22:43:48 EDT 2023
% 0.13/0.35 % CPUTime :
% 114.13/15.07 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 114.13/15.07
% 114.13/15.07 % SZS status Theorem
% 114.13/15.07
% 114.13/15.07 % SZS output start Proof
% 114.13/15.07 Take the following subset of the input axioms:
% 114.13/15.08 fof(conj_0, hypothesis, ?[B_m]: v_na____=c_Groups_Otimes__class_Otimes(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), B_m) => v_thesis____).
% 114.13/15.08 fof(conj_1, conjecture, v_thesis____).
% 114.13/15.08 fof(fact_e, axiom, c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat, v_na____)).
% 114.13/15.08 fof(fact_even__nat__equiv__def2, axiom, ![V_x_2]: (c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat, V_x_2) <=> ?[B_y]: V_x_2=c_Groups_Otimes__class_Otimes(tc_Nat_Onat, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), B_y))).
% 114.13/15.08 fof(fact_numeral__2__eq__2, axiom, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))=c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 114.13/15.08
% 114.13/15.08 Now clausify the problem and encode Horn clauses using encoding 3 of
% 114.13/15.08 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 114.13/15.08 We repeatedly replace C & s=t => u=v by the two clauses:
% 114.13/15.08 fresh(y, y, x1...xn) = u
% 114.13/15.08 C => fresh(s, t, x1...xn) = v
% 114.13/15.08 where fresh is a fresh function symbol and x1..xn are the free
% 114.13/15.08 variables of u and v.
% 114.13/15.08 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 114.13/15.08 input problem has no model of domain size 1).
% 114.13/15.08
% 114.13/15.08 The encoding turns the above axioms into the following unit equations and goals:
% 114.13/15.08
% 114.13/15.08 Axiom 1 (fact_e): c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat, v_na____) = true2.
% 114.13/15.08 Axiom 2 (conj_0): fresh1108(X, X) = true2.
% 114.13/15.08 Axiom 3 (fact_even__nat__equiv__def2_1): fresh109(X, X, Y) = Y.
% 114.13/15.08 Axiom 4 (fact_numeral__2__eq__2): c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 114.13/15.08 Axiom 5 (fact_even__nat__equiv__def2_1): fresh109(c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat, X), true2, X) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), b_y2(X)).
% 114.13/15.08 Axiom 6 (conj_0): fresh1108(v_na____, c_Groups_Otimes__class_Otimes(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), X)) = v_thesis____.
% 114.13/15.08
% 114.13/15.08 Goal 1 (conj_1): v_thesis____ = true2.
% 114.13/15.08 Proof:
% 114.13/15.08 v_thesis____
% 114.13/15.08 = { by axiom 6 (conj_0) R->L }
% 114.13/15.08 fresh1108(v_na____, c_Groups_Otimes__class_Otimes(tc_Nat_Onat, c_Int_Onumber__class_Onumber__of(tc_Nat_Onat, c_Int_OBit0(c_Int_OBit1(c_Int_OPls))), b_y2(v_na____)))
% 114.13/15.08 = { by axiom 4 (fact_numeral__2__eq__2) }
% 114.13/15.08 fresh1108(v_na____, c_Groups_Otimes__class_Otimes(tc_Nat_Onat, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), b_y2(v_na____)))
% 114.13/15.08 = { by axiom 5 (fact_even__nat__equiv__def2_1) R->L }
% 114.13/15.08 fresh1108(v_na____, fresh109(c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat, v_na____), true2, v_na____))
% 114.13/15.08 = { by axiom 1 (fact_e) }
% 114.13/15.08 fresh1108(v_na____, fresh109(true2, true2, v_na____))
% 114.13/15.08 = { by axiom 3 (fact_even__nat__equiv__def2_1) }
% 114.13/15.08 fresh1108(v_na____, v_na____)
% 114.13/15.08 = { by axiom 2 (conj_0) }
% 114.13/15.08 true2
% 114.13/15.08 % SZS output end Proof
% 114.13/15.08
% 114.13/15.08 RESULT: Theorem (the conjecture is true).
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